3.1001 \(\int \frac{(a+b x)^3}{\left (\frac{a d}{b}+d x\right )^3} \, dx\)

Optimal. Leaf size=8 \[ \frac{b^3 x}{d^3} \]

[Out]

(b^3*x)/d^3

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Rubi [A]  time = 0.00730169, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{b^3 x}{d^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^3/((a*d)/b + d*x)^3,x]

[Out]

(b^3*x)/d^3

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Rubi in Sympy [A]  time = 3.76423, size = 7, normalized size = 0.88 \[ \frac{b^{3} x}{d^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**3/(a*d/b+d*x)**3,x)

[Out]

b**3*x/d**3

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Mathematica [A]  time = 0.000525412, size = 8, normalized size = 1. \[ \frac{b^3 x}{d^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^3/((a*d)/b + d*x)^3,x]

[Out]

(b^3*x)/d^3

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Maple [A]  time = 0.002, size = 9, normalized size = 1.1 \[{\frac{{b}^{3}x}{{d}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^3/(a*d/b+d*x)^3,x)

[Out]

b^3*x/d^3

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Maxima [A]  time = 1.33905, size = 11, normalized size = 1.38 \[ \frac{b^{3} x}{d^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^3/(d*x + a*d/b)^3,x, algorithm="maxima")

[Out]

b^3*x/d^3

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Fricas [A]  time = 0.196872, size = 11, normalized size = 1.38 \[ \frac{b^{3} x}{d^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^3/(d*x + a*d/b)^3,x, algorithm="fricas")

[Out]

b^3*x/d^3

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Sympy [A]  time = 0.181287, size = 7, normalized size = 0.88 \[ \frac{b^{3} x}{d^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**3/(a*d/b+d*x)**3,x)

[Out]

b**3*x/d**3

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GIAC/XCAS [A]  time = 0.209472, size = 11, normalized size = 1.38 \[ \frac{b^{3} x}{d^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^3/(d*x + a*d/b)^3,x, algorithm="giac")

[Out]

b^3*x/d^3